Spin-Spin Interaction In Matrix Theory

We calculate the spin dependent static force between two D0-branes in Matrix theory. Supersymmetry relates velocity dependent potentials to spin dependent potentials. The well known v^4/r^7 term is related to a theta^8/r^11 term, where theta is the relative spin of the D0-branes. We calculate this term, confirming that it is the lowest order contribution to the static potential, and find its structure consistent with supergravity.Comment: 15 pages, LaTeX, uses feynmf.sty for diagrams. Reference added and some labels on the diagrams restore

Rhythmic firing patterns in SCN: The role of circuit interactions

The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological extracellular measurements in vitro were made. By means of an interspike interval distribution analysis, it is shown that there is a novel kind of neuronal firing pattern: the harmonic pattern. From these observations, we have developed a theoretical model based on possible filtering processes occurring during synaptic transmission. The model suffices to infer that regular ultradian oscillators could be an emergent property of circuit interactions of cells in the suprachiasmatic nucleus

“Brainland” vs. “flatland”: How many dimensions do we need in brain dynamics?: Comment on the paper “The unreasonable effectiveness of small neural ensembles in high-dimensional brain” by Alexander N. Gorban et al.

In their review article (this issue) [1], Gorban, Makarov and Tyukin develop a successful effort to show in biological, physical and mathematical problems the relevant question of how high-dimensional brain can organise reliable and fast learning in the high-dimensional world of data using reduction tools. In fact, this paper, and several recent studies, focuses on the crucial problem of how the brain manages the information it receives, how it is organized, and how mathematics can learn about this and use dimension related techniques in other fields. Moreover, the opposite problem is also relevant, that is, how we can recover high-dimensional information from low-dimensional ones, the relevant problem of embedding dimensions (the other side of reducing dimensions). The human brain is a real open problem and a great challenge in human knowledge. The way the memory is codified is a fundamental problem in Neuroscience. As mentioned by the authors, the idea of blessing the dimensionality (and the opposite curse of dimensionality), are becoming more and more relevant in machine learning..

The relative dependence of Spanish landscape pattern on environmental and geographical variables over time

The analysis of the dependence of landscape patterns on environment was carried out in order to investigate the landscape structure evolution of Spain. The underlying concept was that the dependence between landscape spatial structure and environmental factors could be gradually decreasing over time. Land cover data were recorded from aerial photo interpretation of 206 4 x 4 km(2) samples from three different years: 1956, 1984 and 1998. Geographical variables were taken into consideration together with the purely environmental ones. General Linear Models of repeated measures were then used to segregate environmental from geographical effects on the pattern of the land cover patches of the samples. Aridity, lithology and topography were the environmental factors used to analyse structural indices of landscape. Landscape composition has a higher dependence on environment than configuration. Environmental variables showed higher correlations with landscape composition and configuration than geographical variables. Ail-long them, overall the climatic aridity and topography significantly accounted for more variation than did lithology. There was a high degree of stability in land cover composition over time, with some significant exceptions. Nevertheless, the registered increase of fragmentation over time has demonstrated that configuration measures are needed to fully assess landscape change

Non-linear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems

The two gap transitions in Ge1−x_{1-x}Snx_x: effect of non-substitutional complex defects

The existence of non-substitutional $\beta$-Sn defects in Ge$_{1-x}$Sn$_{x}$ was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B 81, 155204 (2010)], which established that although most Sn enters substitutionally ($\alpha$-Sn) in the Ge lattice, a second significant fraction corresponds to the Sn-vacancy defect complex in the split-vacancy configuration ( $\beta$-Sn ), in agreement with our previous theoretical study [Ventura et al., Phys. Rev. B 79, 155202 (2009)]. Here, we present our electronic structure calculation for Ge$_{1-x}$Sn$_{x}$, including substitutional $\alpha$-Sn as well as non-substitutional $\beta$-Sn defects. To include the presence of non-substitutional complex defects in the electronic structure calculation for this multi-orbital alloy problem, we extended the approach for the purely substitutional alloy by Jenkins and Dow [Jenkins and Dow, Phys. Rev. B 36, 7994 (1987)]. We employed an effective substitutional two-site cluster equivalent to the real non-substitutional $\beta$-Sn defect, which was determined by a Green's functions calculation. We then calculated the electronic structure of the effective alloy purely in terms of substitutional defects, embedding the effective substitutional clusters in the lattice. Our results describe the two transitions of the fundamental gap of Ge$_{1-x}$Sn$_{x}$ as a function of the total Sn-concentration: namely from an indirect to a direct gap, first, and the metallization transition at higher $x$. They also highlight the role of $\beta$-Sn in the reduction of the concentration range which corresponds to the direct-gap phase of this alloy, of interest for optoelectronics applications.Comment: 11 pages, 9 Figure

Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability

AbstractIn this paper, we concern ourselves with the determination and evaluation of polynomials that are orthogonal with respect to a general discrete Sobolev inner product, that is, an ordinary inner product on the real line plus a finite sum of atomic inner products involving a finite number of derivatives. In a previous paper we provided a complete set of formulas to compute the coefficients of this recurrence. Here, we study the numerical stability of these algorithms for the generation and evaluation of a finite series of Sobolev orthogonal polynomials. Besides, we propose several techniques for reducing and controlling the rounding errors via theoretical running error bounds and a carefully chosen recurrence